Question 1

After 2 years, an investment of $1500 compounded annually at interest rate r will yield $1500 ( 1 + r ) ^ { 2 }$ . Find this product.

Accepted Answer

A)  $r ^ { 2 } + 2 r + 1500$ 
B)  $1500 r ^ { 2 } + 3000 r + 1500$ 
C)  $1500 r ^ { 2 } + 1500 r + 1500$ 
D)  $1500 r ^ { 2 } + 1500$ 
E)  $3000 r ^ { 2 } + 1500 r + 1500$ 
A)  $r ^ { 2 } + 2 r + 1500$ 
B)  $1500 r ^ { 2 } + 3000 r + 1500$ 
C)  $1500 r ^ { 2 } + 1500 r + 1500$ 
D)  $1500 r ^ { 2 } + 1500$ 
E)  $3000 r ^ { 2 } + 1500 r + 1500$

Question 2

The total amount of money accrued from a principal of P dollars invested at r%  simple interest for 13 years is given by $P + 13 r P$ . Factor this expression.

Accepted Answer

A)  $P ( 1 + 13 r )$ 
B)  $14 r P$ 
C)  $r ( P + 13 )$ 
D)  $r ( 1 + 13P)$ 
E)  $P ( r + 13 )$ 
A)  $P ( 1 + 13 r )$ 
B)  $14 r P$ 
C)  $r ( P + 13 )$ 
D)  $r ( 1 + 13P)$ 
E)  $P ( r + 13 )$

Question 3

Factor the expression $9 ( 7 t - 6 ) - 8 t ( 7 t - 6 )$ by factoring out the common binomial factor.

Accepted Answer

A)  $( 7 t - 6 ) ^ { 2 } ( 9 + 8 t )$ 
B)  $( 7 t - 6 ) ( 8 t - 9 + 1 )$ 
C)  $( 7 t - 6 ) ( 9 + 8 t )$ 
D)  $( 7 t - 6 ) ^ { 2 } ( 9 - 8 t )$ 
E)  $( 7 t - 6 ) ( 9 - 8 t )$ 
A)  $( 7 t - 6 ) ^ { 2 } ( 9 + 8 t )$ 
B)  $( 7 t - 6 ) ( 8 t - 9 + 1 )$ 
C)  $( 7 t - 6 ) ( 9 + 8 t )$ 
D)  $( 7 t - 6 ) ^ { 2 } ( 9 - 8 t )$ 
E)  $( 7 t - 6 ) ( 9 - 8 t )$

Question 4

Write a simplified expression for the area of the shaded region of the figure below.

Accepted Answer

A)  $\text { 3. } 5 x ^ { 2 } + 14 x$ 
B)  $4.5 x ^ { 2 } + 14.5 x$ 
C)  $3.5 x ^ { 2 } + 10.5 x$ 
D)  $4.5 x ^ { 2 } + 9 x$ 
E)  $3.5 x ^ { 2 } + 7 x$ 
A)  $\text { 3. } 5 x ^ { 2 } + 14 x$ 
B)  $4.5 x ^ { 2 } + 14.5 x$ 
C)  $3.5 x ^ { 2 } + 10.5 x$ 
D)  $4.5 x ^ { 2 } + 9 x$ 
E)  $3.5 x ^ { 2 } + 7 x$

Question 5

Evaluate the expression $\left( \frac { 5 x } { 3 y } \right) ^ { - 1 }$ when x=-8 and y=9 .

Accepted Answer

A)  $- \frac { 27 } { 40 }$ 
B)  $\frac { 40 } { 27 }$ 
C)  $\frac { 27 } { 40 }$ 
D)  $- \frac { 40 } { 27 }$ 
E)  $- \frac { 15 } { 8 }$ 
A)  $- \frac { 27 } { 40 }$ 
B)  $\frac { 40 } { 27 }$ 
C)  $\frac { 27 } { 40 }$ 
D)  $- \frac { 40 } { 27 }$ 
E)  $- \frac { 15 } { 8 }$

Question 6

Write, in factored form, an expression for the area of the shaded region of the figure below where m is $8$ and n is $18$ .

Accepted Answer

A)  $4 ( 6 - x ) ( 6 + x )$ 
B)  $( 12 - x ) ( 12 - x )$ 
C)  $4 ( 4 - x ) ( 9 - x )$ 
D)  $( 12 + x ) ^ { 2 }$ 
E)  $4 ( 4 + x ) ( 9 - x )$ 
A)  $4 ( 6 - x ) ( 6 + x )$ 
B)  $( 12 - x ) ( 12 - x )$ 
C)  $4 ( 4 - x ) ( 9 - x )$ 
D)  $( 12 + x ) ^ { 2 }$ 
E)  $4 ( 4 + x ) ( 9 - x )$

Question 7

Fill in the missing factor. $y ^ { 2 } - y - 210 = ( y + 14 ) ( - )$

Accepted Answer

A)  $y - 15$ 
B)  $15 - y$ 
C)  $y + 15$ 
D)  $y + 14$ 
E)  $y - 14$ 
A)  $y - 15$ 
B)  $15 - y$ 
C)  $y + 15$ 
D)  $y + 14$ 
E)  $y - 14$

Question 8

Solve the equation below by factoring. $2 x ^ { 2 } = 74 x$

Accepted Answer

A)  $- 37$ , 37 
B) 37 
C)  $148$ 
D)  $0,74$ 
E)  $0,37$ 
A)  $- 37$ , 37 
B) 37 
C)  $148$ 
D)  $0,74$ 
E)  $0,37$

Question 9

Multiply $( 8 x - 8 ) ( 3 x - 4 )$ and simplify.

Accepted Answer

A)  $24 x ^ { 2 } - 56 x + 32$ 
B)  $24 x + 32$ 
C)  $24 x ^ { 2 } - 16 x + 32$ 
D)  $24 x ^ { 2 } + 11 x + 32$ 
E)  $24 x ^ { 2 } + 32$ 
A)  $24 x ^ { 2 } - 56 x + 32$ 
B)  $24 x + 32$ 
C)  $24 x ^ { 2 } - 16 x + 32$ 
D)  $24 x ^ { 2 } + 11 x + 32$ 
E)  $24 x ^ { 2 } + 32$

Question 10

Find the height in feet of a free-falling object at time t=2 using the function $s = - 16 t ^ { 2 } + 57 t + 53$ .

Accepted Answer

A) 125 feet 
B) 231 feet 
C) 50 feet 
D) 3 feet 
E) 103 feet 
A) 125 feet 
B) 231 feet 
C) 50 feet 
D) 3 feet 
E) 103 feet

Question 11

Factor the difference of two squares. $49 - 64 x ^ { 2 }$

Accepted Answer

A)  $( 8 + 7 x ) ^ { 2 }$ 
B)  $( 7 - 8 x ) ^ { 2 }$ 
C)  $( 7 + 8 x ) ^ { 2 }$ 
D)  $( 8 + 7 x ) ( 8 - 7 x )$ 
E)  $( 7 + 8 x ) ( 7 - 8 x )$ 
A)  $( 8 + 7 x ) ^ { 2 }$ 
B)  $( 7 - 8 x ) ^ { 2 }$ 
C)  $( 7 + 8 x ) ^ { 2 }$ 
D)  $( 8 + 7 x ) ( 8 - 7 x )$ 
E)  $( 7 + 8 x ) ( 7 - 8 x )$

Question 12

Solve the equation below by factoring. $$x ^ { 3 } + 5 x ^ { 2 } - 36 x = 0$$

Accepted Answer

A)  $x = 4$ and $x = 9$ 
B)  $x = - 9$ , $x = 0$ and $x = 4$ 
C)  $x = - 4$ , $x = 0$ and $x = 9$ 
D)  $x = - 9$ , $x = - 4$ and $x = 0$ 
E)  $x = 0$ , $x = 4$ and $x = 9$ 
A)  $x = 4$ and $x = 9$ 
B)  $x = - 9$ , $x = 0$ and $x = 4$ 
C)  $x = - 4$ , $x = 0$ and $x = 9$ 
D)  $x = - 9$ , $x = - 4$ and $x = 0$ 
E)  $x = 0$ , $x = 4$ and $x = 9$

Question 13

Find the greatest common factor of the expressions below, if one exists. $40 ( 7 - y ) ^ { 5 } , 50 ( 7 - y ) ^ { 4 }$

Accepted Answer

A)  $40 ( 7 - y ) ^ { 4 }$ 
B)  $5 ( 7 - y ) ^ { 10 }$ 
C)  $10 ( 7 - y ) ^ { 4 }$ 
D)  $4 ( 7 - y ) ^ { 5 }$ 
E) No greatest common monomial factor exists. 
A)  $40 ( 7 - y ) ^ { 4 }$ 
B)  $5 ( 7 - y ) ^ { 10 }$ 
C)  $10 ( 7 - y ) ^ { 4 }$ 
D)  $4 ( 7 - y ) ^ { 5 }$ 
E) No greatest common monomial factor exists.

Question 14

Find a real number c such that the expression $x ^ { 2 } - 14 x + c$ is a perfect square trinomial.

Accepted Answer

A)  9 
B)  49 
C)  59 
D)  69 
E)  99 
A)  9 
B)  49 
C)  59 
D)  69 
E)  99

Question 15

Factor the polynomial $y ^ { 2 } - 4 y + 3 y - 12$ by grouping.

Accepted Answer

A)  $3 y ( y - 5 )$ 
B)  $( y - 4 ) ( y - 3 )$ 
C)  $3 y ( y - 4 ) ^ { 2 }$ 
D)  $( y - 4 ) ( y - 12 )$ 
E)  $( y - 4 ) ( y + 3 )$ 
A)  $3 y ( y - 5 )$ 
B)  $( y - 4 ) ( y - 3 )$ 
C)  $3 y ( y - 4 ) ^ { 2 }$ 
D)  $( y - 4 ) ( y - 12 )$ 
E)  $( y - 4 ) ( y + 3 )$

Question 16

The revenue R from the sale of x cameras is given by $R = 65 x - x ^ { 2 }$ . The cost C of producing x cameras is given by $C = 91 + 45 x$ . How many cameras must be produced and sold in order to break even?

Accepted Answer

A) 7 cameras 
B) 8 cameras 
C) 10 cameras 
D) 15 cameras 
E) 19 cameras 
A) 7 cameras 
B) 8 cameras 
C) 10 cameras 
D) 15 cameras 
E) 19 cameras

Question 17

Factor a negative real number out of the polynomial 12-x and then write the polynomial factor in standard form.

Accepted Answer

A)  x+12 
B)  -(x-12) 
C)  -(12-x) 
D)  x-12 
E)  -(x+12) 
A)  x+12 
B)  -(x-12) 
C)  -(12-x) 
D)  x-12 
E)  -(x+12)

Question 18

Use the rules of exponents to simplify the expression below. $\frac { x ^ { 4 n + 4 } y ^ { 5 n - 5 } } { x ^ { 3 n + 2 } y ^ { n - 2 } }$

Accepted Answer

A)  $x ^ { n + 2 } y ^ { 4 n - 7 }$ 
B)  $x ^ { n + 6 } y ^ { 4 n - 3 }$ 
C)  $x ^ { 7 n + 2 } y ^ { 4 x - 3 }$ 
D)  $x ^ { n + 2 } y ^ { 4 n - 3 }$ 
E)  $x ^ { 7n+ 2 } y ^ { 4 n - 7 }$ 
A)  $x ^ { n + 2 } y ^ { 4 n - 7 }$ 
B)  $x ^ { n + 6 } y ^ { 4 n - 3 }$ 
C)  $x ^ { 7 n + 2 } y ^ { 4 x - 3 }$ 
D)  $x ^ { n + 2 } y ^ { 4 n - 3 }$ 
E)  $x ^ { 7n+ 2 } y ^ { 4 n - 7 }$

Question 19

Factor a negative real number out of the polynomial $5 y - 5 - 25 y ^ { 2 }$ and then write the polynomial factor in standard form.

Accepted Answer

A)  $- 5 \left( 5 y ^ { 2 } - y + 1 \right)$ 
B)  $- \left( 25 y ^ { 2 } + y + 5 \right)$ 
C)  $- 5 \left( 5 y ^ { 2 } + y - 5 \right)$ 
D)  $- 5 \left( 5 y ^ { 2 } + 5 y + 1 \right)$ 
E)  $- \left( 25 y ^ { 2 } - 5 y + 1 \right)$ 
A)  $- 5 \left( 5 y ^ { 2 } - y + 1 \right)$ 
B)  $- \left( 25 y ^ { 2 } + y + 5 \right)$ 
C)  $- 5 \left( 5 y ^ { 2 } + y - 5 \right)$ 
D)  $- 5 \left( 5 y ^ { 2 } + 5 y + 1 \right)$ 
E)  $- \left( 25 y ^ { 2 } - 5 y + 1 \right)$

Question 20

Solve the equation below by factoring. $a ^ { 2 } + 8 a + 25 = 9$

Accepted Answer

A)  $a = - 4$ and $a = 0$ 
B)  $a = - 4$ 
C)  $a = 0$ and $a = 4$ 
D)  $a = - 4$ and $a = 4$ 
E)  $a = 4$ 
A)  $a = - 4$ and $a = 0$ 
B)  $a = - 4$ 
C)  $a = 0$ and $a = 4$ 
D)  $a = - 4$ and $a = 4$ 
E)  $a = 4$

After 2 years, an investment of $1500 compounded annually at interest rate r will yield $1500 ( 1 + r ) ^ { 2 }$ . Find this product.

The total amount of money accrued from a principal of P dollars invested at r% simple interest for 13 years is given by $P + 13 r P$ . Factor this expression.

Factor the expression $9 ( 7 t - 6 ) - 8 t ( 7 t - 6 )$ by factoring out the common binomial factor.

Write a simplified expression for the area of the shaded region of the figure below.

Evaluate the expression $\left( \frac { 5 x } { 3 y } \right) ^ { - 1 }$ when x=-8 and y=9 .

Write, in factored form, an expression for the area of the shaded region of the figure below where m is $8$ and n is $18$ .

Fill in the missing factor. $y ^ { 2 } - y - 210 = ( y + 14 ) ( - )$

Solve the equation below by factoring. $2 x ^ { 2 } = 74 x$

Multiply $( 8 x - 8 ) ( 3 x - 4 )$ and simplify.

Find the height in feet of a free-falling object at time t=2 using the function $s = - 16 t ^ { 2 } + 57 t + 53$ .

Factor the difference of two squares. $49 - 64 x ^ { 2 }$

Solve the equation below by factoring. $x ^ { 3 } + 5 x ^ { 2 } - 36 x = 0$

Find the greatest common factor of the expressions below, if one exists. $40 ( 7 - y ) ^ { 5 } , 50 ( 7 - y ) ^ { 4 }$

Find a real number c such that the expression $x ^ { 2 } - 14 x + c$ is a perfect square trinomial.

Factor the polynomial $y ^ { 2 } - 4 y + 3 y - 12$ by grouping.

The revenue R from the sale of x cameras is given by $R = 65 x - x ^ { 2 }$ . The cost C of producing x cameras is given by $C = 91 + 45 x$ . How many cameras must be produced and sold in order to break even?

Factor a negative real number out of the polynomial 12-x and then write the polynomial factor in standard form.

Use the rules of exponents to simplify the expression below. $\frac { x ^ { 4 n + 4 } y ^ { 5 n - 5 } } { x ^ { 3 n + 2 } y ^ { n - 2 } }$

Factor a negative real number out of the polynomial $5 y - 5 - 25 y ^ { 2 }$ and then write the polynomial factor in standard form.

Solve the equation below by factoring. $a ^ { 2 } + 8 a + 25 = 9$

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Exam 5: Polynomials and Factoring

After 2 years, an investment of $1500 compounded annually at interest rate r will yield 1500(1+r)21500 ( 1 + r ) ^ { 2 }1500(1+r)2 . Find this product.

The total amount of money accrued from a principal of P dollars invested at r% simple interest for 13 years is given by P+13rPP + 13 r PP+13rP . Factor this expression.

Factor the expression 9(7t−6)−8t(7t−6)9 ( 7 t - 6 ) - 8 t ( 7 t - 6 )9(7t−6)−8t(7t−6) by factoring out the common binomial factor.

Write a simplified expression for the area of the shaded region of the figure below.

Evaluate the expression (5x3y)−1\left( \frac { 5 x } { 3 y } \right) ^ { - 1 }(3y5x​)−1 when x=-8 and y=9 .

Write, in factored form, an expression for the area of the shaded region of the figure below where m is 888 and n is 181818 .

Fill in the missing factor. y2−y−210=(y+14)(−)y ^ { 2 } - y - 210 = ( y + 14 ) ( - )y2−y−210=(y+14)(−)

Solve the equation below by factoring. 2x2=74x2 x ^ { 2 } = 74 x2x2=74x

Multiply (8x−8)(3x−4)( 8 x - 8 ) ( 3 x - 4 )(8x−8)(3x−4) and simplify.

Find the height in feet of a free-falling object at time t=2 using the function s=−16t2+57t+53s = - 16 t ^ { 2 } + 57 t + 53s=−16t2+57t+53 .

Factor the difference of two squares. 49−64x249 - 64 x ^ { 2 }49−64x2

Solve the equation below by factoring. x3+5x2−36x=0x ^ { 3 } + 5 x ^ { 2 } - 36 x = 0x3+5x2−36x=0

Find the greatest common factor of the expressions below, if one exists. 40(7−y)5,50(7−y)440 ( 7 - y ) ^ { 5 } , 50 ( 7 - y ) ^ { 4 }40(7−y)5,50(7−y)4

Find a real number c such that the expression x2−14x+cx ^ { 2 } - 14 x + cx2−14x+c is a perfect square trinomial.

Factor the polynomial y2−4y+3y−12y ^ { 2 } - 4 y + 3 y - 12y2−4y+3y−12 by grouping.

The revenue R from the sale of x cameras is given by R=65x−x2R = 65 x - x ^ { 2 }R=65x−x2 . The cost C of producing x cameras is given by C=91+45xC = 91 + 45 xC=91+45x . How many cameras must be produced and sold in order to break even?

Factor a negative real number out of the polynomial 12-x and then write the polynomial factor in standard form.

Use the rules of exponents to simplify the expression below. x4n+4y5n−5x3n+2yn−2\frac { x ^ { 4 n + 4 } y ^ { 5 n - 5 } } { x ^ { 3 n + 2 } y ^ { n - 2 } }x3n+2yn−2x4n+4y5n−5​

Factor a negative real number out of the polynomial 5y−5−25y25 y - 5 - 25 y ^ { 2 }5y−5−25y2 and then write the polynomial factor in standard form.

Solve the equation below by factoring. a2+8a+25=9a ^ { 2 } + 8 a + 25 = 9a2+8a+25=9

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

After 2 years, an investment of $1500 compounded annually at interest rate r will yield $1500 ( 1 + r ) ^ { 2 }$ . Find this product.

The total amount of money accrued from a principal of P dollars invested at r% simple interest for 13 years is given by $P + 13 r P$ . Factor this expression.

Factor the expression $9 ( 7 t - 6 ) - 8 t ( 7 t - 6 )$ by factoring out the common binomial factor.

Evaluate the expression $\left( \frac { 5 x } { 3 y } \right) ^ { - 1 }$ when x=-8 and y=9 .

Write, in factored form, an expression for the area of the shaded region of the figure below where m is $8$ and n is $18$ .

Fill in the missing factor. $y ^ { 2 } - y - 210 = ( y + 14 ) ( - )$

Solve the equation below by factoring. $2 x ^ { 2 } = 74 x$

Multiply $( 8 x - 8 ) ( 3 x - 4 )$ and simplify.

Find the height in feet of a free-falling object at time t=2 using the function $s = - 16 t ^ { 2 } + 57 t + 53$ .

Factor the difference of two squares. $49 - 64 x ^ { 2 }$

Solve the equation below by factoring. $x ^ { 3 } + 5 x ^ { 2 } - 36 x = 0$

Find the greatest common factor of the expressions below, if one exists. $40 ( 7 - y ) ^ { 5 } , 50 ( 7 - y ) ^ { 4 }$

Find a real number c such that the expression $x ^ { 2 } - 14 x + c$ is a perfect square trinomial.

Factor the polynomial $y ^ { 2 } - 4 y + 3 y - 12$ by grouping.

The revenue R from the sale of x cameras is given by $R = 65 x - x ^ { 2 }$ . The cost C of producing x cameras is given by $C = 91 + 45 x$ . How many cameras must be produced and sold in order to break even?

Use the rules of exponents to simplify the expression below. $\frac { x ^ { 4 n + 4 } y ^ { 5 n - 5 } } { x ^ { 3 n + 2 } y ^ { n - 2 } }$

Factor a negative real number out of the polynomial $5 y - 5 - 25 y ^ { 2 }$ and then write the polynomial factor in standard form.

Solve the equation below by factoring. $a ^ { 2 } + 8 a + 25 = 9$